How to play an animation on a mesh?
Blender Internal:


Add a new texture and set the type to image or movie.
Select a file, then set the source to either Sequence or Movie depending on the format your rendered animation is in. (e.g. Sequence for an image sequence, or Movie for a single video file.)


Cycles:


Add a new Image Texture node and open a file.
Set the Source (this option will appear after you select a file) to either Sequence or Movie, again depending on the format your rendered animation is in.